CPM Homework Help : ACC7 Problem 9-33

Based on the given information, determine which pairs of lines, if any, are parallel. If none are necessarily parallel, write “none.”

Hint:

Alternate interior angles and corresponding angles are equal only if the lines cut by the transversal are parallel.
Conversely, if the angles are equal the lines must be parallel.

$m∠2 = m∠7$
Hint (a):
These are alternate interior angles.
$m∠3 = m∠11$
Hint (b):
These are corresponding angles.
Answer (b):
$e$ and $f$
$m∠1 = m∠12$
Hint (c):
In the diagram below, angles 1 and 12 are equal.
Do any two lines look parallel?
$m∠13 = m∠12$
Hint (d):
Vertical angles are always equal.
Answer (d):
$c$ and $d$
$∠6$ and $∠7$ are supplementary.
Hint (e):
Angle 6 would be supplementary to angle 7 if angle 7 was equal to angle 2.

Two increasing transversal lines, c, and d, cross two horizontal lines, e, and f, creating 4 points of intersection. The angles at each intersection are labeled, starting at the top left and going clockwise as follows: Intersection of c, and e: 1, 2, 6, and 5. Intersection of, d, and e: 3, 4, 8, and 7. Intersection of c, and f: 9, 10, 14, and 13. Intersection of, d, and f: 11, 12, 16, and 15.